North East School Division
Unpacking Outcomes
Unpacking the Outcome
Demonstrate  arithmetic sequences
 arithmetic series
 geometric series
 geometric series
Outcome (circle the verb and underline the qualifiers)
P20.10 Demonstrate understanding of arithmetic and geometric (finite and infinite) sequences and series.
KNOW
Vocabulary: sequence,
arithmetic, common
difference, general term,
series, geometric,
common ratio, convergent
series, divergent series,
infinite geometric series
UNDERSTAND
That trending analysis is
often related to arithmetic
and/or geometric sequences
and series.
That patterns have an effect
on decision making.
That a sequence is an
ordered list of elements.
That an arithmetic sequence
has a common difference.
That a geometric sequence
has a common ratio.
That an infinite geometric
series has an infinite
number of terms, but can
still be convergent.
BE ABLE TO DO
a. Identify assumptions made in determining that a sequence or series is either
arithmetic or geometric.
b. Provide an example of a sequence that follows an identifiable pattern, but that is
neither arithmetic nor geometric.
c. Provide an example of an arithmetic or geometric sequence that is relevant to
one’s self, family, or community.
d. Generate arithmetic or geometric sequences from provided information.
e. Develop, generalize, explain, and apply a rule and other strategies for determining
the values of t₁, a, d, n, or tn in situational questions that involve arithmetic
sequences.
f. Develop, generalize, explain, and apply a rule and other strategies for determining
the values of t₁, a, d, n, or Sn in situational questions that involve arithmetic series.
g. Solve situational questions that involve arithmetic sequences and series.
h. Develop, generalize, explain, and apply a rule and other strategies for determining
the values of t₁, a, r, n, or tn in situational questions that involve geometric
sequences.
i. Develop, generalize, explain, and apply a rule and other strategies for determining
the values of t₁, a, r, n, or Sn in situational questions that involve geometric series.
j. Develop, generalize, and explain a rule and strategies for determining the sum of an
infinite geometric series and apply this knowledge to the solving of situational
questions.
k. Analyze a geometric series to determine if it is convergent or divergent and explain
the reasoning.
ESSENTIAL QUESTIONS
1. How do I add an infinite number of numbers?
2. How do arithmetic sequences and series apply to the real world?
3. How do geometric sequences and series apply to the real world?
4. What is the difference between a sequence and a series?
5. Why can an infinite geometric series have a finite sum?